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Multiscale Modelling. Mateusz Sitko. Faculty of Metals Engineering and Industrial Computer Science Department of Applied Computer Science and Modelling  Kraków 11 -03-2014. Mateusz Sitko B5*607 consultation: Tuesday 1 3 :00 – 1 4 :00. Classes calendar. 2 reports:

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multiscale modelling

Multiscale Modelling

Mateusz Sitko

Faculty of Metals Engineering and Industrial Computer ScienceDepartment of Applied Computer Science and Modelling Kraków 11-03-2014


Mateusz Sitko



Tuesday 13:00 – 14:00


2 reports:

    • 1st – Grain growth algorithm modification (Cellular automata, Monte Carlo)
    • 2nd – Monte Carlo static recrystallization algorithm + grid infrastructure
  • Final degree will be positive if each report gets min 3.0
  • 2 unexcused absences (remainder – medical leave)

CA method

The main idea of the cellular automata technique is to divide a specific part of the material into one-, two-, or three-dimensional lattices of finite cells, where cells have clearly defined interaction rules between each other. Each cell in this space is called a cellular automaton, while the lattice of the cells is known as cellular automata space.

  • CA space - finite set of cells, where each cell is described by a set of internal variables describing the state of a cell.
  • Neighborhood – describes the closest neighbors of a particular cell. It can be in 1D, 2D and 3D space.
  • Transition rules - f, the state of each cell in the lattice is determined by the previous states of its neighbors and the cell itself by the f function


N(i) – neighbours of the ith cell, i – state of the ith cell


Simple Grain Growth CA algorithm

2 grains

Von Neumann neighborhood

Initial space

1st step

2nd step

last step


Boundary conditions

•absorbing boundary conditions – the state of cells located on the edges of the CA space are properly fixed with a specific state to absorb moving quantities.

•periodic boundary conditions – the CA neighborhood is properly defined and take into account cells located on subsequent edges of the CA space.



1. At the beginning of simulation (square diagonal d and circle with radius r).

2. After simulation (square with diagonal d and circle with radius r).

Initial space

1st step

last step

2nd step